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Research Article

The Trend-Renewal Process for Statistical Analysis of Repairable Systems

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Pages 31-44 | Published online: 01 Jan 2012

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Sareh Goli & Safieh Mahmoodi. (2023) Residual Lifetime of Repairable Systems and Phase type Approximation. Quality Technology & Quantitative Management 0:0, pages 1-24.
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Lochana K. Palayangoda, Ronald W. Butler, Hon Keung Tony Ng, Fangfang Yang & Kwok Leung Tsui. (2022) Evaluation of mean-time-to-failure based on nonlinear degradation data with applications. IISE Transactions 54:3, pages 286-302.
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Ghislain Léveillé & Emmanuel Hamel. (2019) Compound trend renewal process with discounted claims: a unified approach. Scandinavian Actuarial Journal 2019:3, pages 228-246.
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Zhibing Xu, Yili Hong, William Q. Meeker, Brock E. Osborn & Kati Illouz. (2017) A Multi-Level Trend-Renewal Process for Modeling Systems With Recurrence Data. Technometrics 59:2, pages 225-236.
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Weiwen Peng, Narayanaswamy Balakrishnan & Hong-Zhong Huang. (2018) Reliability modelling and assessment of a heterogeneously repaired system with partially relevant recurrence data. Applied Mathematical Modelling 59, pages 696-712.
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A. H. S. Garmabaki, Alireza Ahmadi, Yasser A. Mahmood & Abbas Barabadi. (2015) Reliability Modelling of Multiple Repairable Units. Quality and Reliability Engineering International 32:7, pages 2329-2343.
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Vaclav Slimacek & Bo Henry Lindqvist. (2016) Nonhomogeneous Poisson process with nonparametric frailty. Reliability Engineering & System Safety 149, pages 14-23.
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F. Q. Yuan & J. M. Lu. (2015) Imperfect repair model for complex repairable system - a literature survey with discussion. Imperfect repair model for complex repairable system - a literature survey with discussion.
Yasuhiro Saito & Tadashi Dohi. (2015) Robustness of Non-homogeneous Gamma Process-Based Software Reliability Models. Robustness of Non-homogeneous Gamma Process-Based Software Reliability Models.
Haitao Liao & Huairui Guo. 2015. Through-life Engineering Services. Through-life Engineering Services 157 174 .
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Crossref
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Crossref
Ma. Zenia N. Agustin. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
Shunichi Nomura, Yosihiko Ogata & Robert M. Nadeau. (2014) Space-time model for repeating earthquakes and analysis of recurrence intervals on the San Andreas Fault near Parkfield, California. Journal of Geophysical Research: Solid Earth 119:9, pages 7092-7122.
Crossref
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Crossref
Thomas M. Welte & Kesheng Wang. (2014) Models for lifetime estimation: an overview with focus on applications to wind turbines. Advances in Manufacturing 2:1, pages 79-87.
Crossref
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Rong-Tsorng Wang. 2014. Energy-Efficient Fault-Tolerant Systems. Energy-Efficient Fault-Tolerant Systems 11 97 .
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Crossref
V Slimacek & B Lindqvist. 2013. Safety, Reliability and Risk Analysis. Safety, Reliability and Risk Analysis 1229 1233 .
Emmanuel Remy, Franck Corset, Stéphane Despréaux, Laurent Doyen & Olivier Gaudoin. (2013) An example of integrated approach to technical and economic optimization of maintenance. Reliability Engineering & System Safety 116, pages 8-19.
Crossref
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Crossref
Zhi-Sheng Ye, Min Xie & Loon-Ching Tang. (2013) Reliability evaluation of hard disk drive failures based on counting processes. Reliability Engineering & System Safety 109, pages 110-118.
Crossref
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Crossref
Alicja Jokiel-Rokita & Ryszard Magiera. (2011) Estimation of parameters for trend-renewal processes. Statistics and Computing 22:2, pages 625-637.
Crossref
M.J. Fadaee & R. Tabatabaei. (2011) RETRACTED: Estimation of failure probability in water pipes network using statistical model. Engineering Failure Analysis 18:4, pages 1184-1192.
Crossref
Satadal Ghosh & Sujit K. Majumdar. (2011) Reliability modeling and prediction using classical and Bayesian approach. International Journal of Quality & Reliability Management 28:5, pages 556-586.
Crossref
Bo H. Lindqvist & Bjarte Rannestad. (2011) Monte Carlo exact goodness-of-fit tests for nonhomogeneous Poisson processes. Applied Stochastic Models in Business and Industry 27:3, pages 329-341.
Crossref
F. G. Badia. (2016) Hazard Rate Properties of a General Counting Process Stopped at an Independent Random Time. Journal of Applied Probability 48:1, pages 56-67.
Crossref
F. G. Badia. (2016) Hazard Rate Properties of a General Counting Process Stopped at an Independent Random Time. Journal of Applied Probability 48:01, pages 56-67.
Crossref
M. Luz Gámiz, K. B. Kulasekera, Nikolaos Limnios & Bo Henry LindqvistM. Luz Gámiz, K. B. Kulasekera, Nikolaos Limnios & Bo Henry Lindqvist. 2011. Applied Nonparametric Statistics in Reliability. Applied Nonparametric Statistics in Reliability 93 118 .
E. Beutner & E. Cramer. (2010) NONPARAMETRIC META‐ANALYSIS FOR MINIMAL‐REPAIR SYSTEMS. Australian & New Zealand Journal of Statistics 52:4, pages 383-401.
Crossref
Jennifer S. K. Chan & Doris Y. P. Leung. (2010) Binary geometric process model for the modeling of longitudinal binary data with trend. Computational Statistics 25:3, pages 505-536.
Crossref
M. S. Bebbington. (2010) Trends and clustering in the onsets of volcanic eruptions. Journal of Geophysical Research: Solid Earth 115:B1.
Crossref
Bo Henry Lindqvist. 2010. Mathematical and Statistical Models and Methods in Reliability. Mathematical and Statistical Models and Methods in Reliability 277 288 .
Kajsa Kvist, Per Kragh Andersen, Jules Angst & Lars Vedel Kessing. (2008) Repeated events and total time on test. Statistics in Medicine 27:19, pages 3817-3832.
Crossref
David F. Percy. 2008. Complex System Maintenance Handbook. Complex System Maintenance Handbook 179 207 .
Bo Henry Lindqvist. 2008. Complex System Maintenance Handbook. Complex System Maintenance Handbook 235 261 .
Ma. Zenia N. Agustin. 2007. Encyclopedia of Statistics in Quality and Reliability. Encyclopedia of Statistics in Quality and Reliability.
Edsel A. Peña, Elizabeth H. Slate & Juan R. González. (2007) Semiparametric inference for a general class of models for recurrent events. Journal of Statistical Planning and Inference 137:6, pages 1727-1747.
Crossref
Knut Heggland & Bo H. Lindqvist. (2007) A non-parametric monotone maximum likelihood estimator of time trend for repairable system data. Reliability Engineering & System Safety 92:5, pages 575-584.
Crossref
Bo Henry Lindqvist. (2006) On the Statistical Modeling and Analysis of Repairable Systems. Statistical Science 21:4.
Crossref
Edsel A. Peña. (2006) Dynamic Modeling and Statistical Analysis of Event Times. Statistical Science 21:4.
Crossref
Huairui Guo, Wenbiao Wenbiao Zhao & A. Mettas. (2006) Practical methods for modeling repairable systems with time trends and repair effects. Practical methods for modeling repairable systems with time trends and repair effects.

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